WorksheetsCongruent and Similar Figures
Total questions: 74
Worksheet time: 2hrs 45mins
Name
Class
Date
1.
All angles in similar figures are congruent.
a)
True
b)
False
2.
Are the following similar? Why or why not?
a)
Yes
b)
No, the corresponding angles are not equal.
c)
No, the ratios of the corresponding sides are not equal.
3.
The pair of figures is similar. Find the missing side.
a)
x = 12
b)
x = 3
c)
x = 40
d)
x = 4
4.
The pair of figures is similar. Find the missing side.
a)
x = 20
b)
x = 12
c)
x = 5
d)
x = 4
5.
A rectangular garden is 45 ft wide and 70 ft long. On a blueprint, the width is 9 in. Identify the length on the blueprint.
a)
7 in
b)
9 in
c)
12 in
d)
14 in
6.
Tell whether the two figures are congruent.
a)
Yes, same size and same shape
b)
No, same shape but different sizes
c)
No, different size and different shapes
7.
∠A = ≅
a)
∠M
b)
∠N
c)
∠L
8.
∠U = ≅
a)
∠F
b)
∠G
c)
∠E
9.
FD = ≅
a)
IK
b)
KJ
c)
JI
d)
EF
10.
a)
A
b)
C
c)
D
11.
a)
3 inches
b)
5 inches
c)
90 inches
d)
4 inches
12.
a)
4m
b)
5m
c)
3m
d)
4.5m
13.
The triangles are congruent. Which of the following statements must be true?
a)
∠A ≅ ∠D
b)
∠B ≅ ∠E
c)
AB ≅ DE
d)
BC ≅ FD
14.
The figures are congruent. Name one pair of corresponding angles.
a)
Q and W
b)
R and Z
c)
S and Z
d)
T and P
15.
If ∆LMK ≅ ∆LMT, then
∠K ≅ ____
∠K ≅ ____
a)
T
b)
∠T
c)
∠M
d)
∠L
16.
Remember order matters. Which of the following is true?
a)
∆JLK ≅ ∆XWJ
b)
∆LJK ≅ ∆JWX
c)
∆JKL ≅ ∆JXW
d)
∆LKJ ≅ ∆JXW
17.
If ∆XYZ ≅ ∆KLM, then
∠Y≅ _____
∠Y≅ _____
a)
∠K
b)
∠M
c)
∠L
d)
∠Z
18.
Determine the relationship of the figures.
a)
Congruent
b)
Not Congruent
c)
Similar
19.
Determine the relationship of the figures.
a)
Congruent
b)
Not Congruent
c)
Similar
20.
Determine the relationship of the figures.
a)
Congruent
b)
Not Congruent
c)
Similar
21.
Determine the relationship of the figures.
a)
Congruent
b)
Not Congruent
c)
Similar
22.
Determine the relationship of the figures.
a)
Congruent
b)
Not Congruent
c)
Similar
23.
FD = ≅
a)
IK
b)
KJ
c)
JI
d)
EF
24.
∠A = ≅
a)
∠M
b)
∠N
c)
∠L
25.
∠U = ≅
a)
∠F
b)
∠G
c)
∠E
26.
∠W = ≅
a)
∠I
b)
∠G
c)
∠H
27.
∆JIK ≅
a)
∆TRS
b)
∆RST
c)
∆STR
d)
∆TSR
28.
∆ISR ≅
a)
∆TRS
b)
∆RST
c)
∆STR
d)
∆TSR
29.
∠P≅
a)
∠J
b)
∠M
c)
∠T
30.
m∠P=
a)
73
b)
48
c)
59
31.
m∠J=
a)
73
b)
48
c)
59
32.
JM=≅
a)
HS
b)
PH
c)
PS
33.
MT=
a)
5
b)
8
c)
12
34.
x =
a)
90°
b)
65°
c)
25°
35.
x =
a)
60
b)
70
c)
50
d)
25
36.
x =
a)
87
b)
42
c)
17
d)
8
37.
x =
a)
24
b)
40
c)
32
38.
x =
a)
9
b)
10
c)
12
39.
x =
a)
7
b)
8
40.
x =
a)
9
b)
11
c)
17
41.
If ∆PIG ≅ ∆COW, ∠P≅∠?
a)
C
b)
O
c)
W
42.
a)
A
b)
B
c)
C
d)
D
43.
All angles in similar figures are congruent.
a)
True
b)
False
44.
Sides in similar figures must be proportional.
a)
True
b)
False
45.
Gwen scans a photo that is 4 in. wide by 6 in. long into her computer. If she scales the length down to 3 in., how wide should the similar photo be?
a)
3 in
b)
2 in.
c)
4 in
d)
1 in
46.
A picture of a school’s mascot is 18 in. wide and 24 in. long. It is enlarged proportionally to banner size. If the width is enlarged to 54 in., what is the length of the banner?
a)
72 in
b)
60 in
c)
62 in
d)
80 in
47.
A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby casts a shadow that measures 24 feet. How tall is the building? (Draw a picture, set up a proportion)
a)
24 feet
b)
21 feet
c)
27 feet
d)
32 feet
48.
Find the missing side of the large triangle, then, find the PERIMETER of the large triangle.
a)
the missing side is 12, the perimeter is 24
b)
the missing side is 12, the perimeter is 36
49.
The pair of figures is similar. Find the missing side.
a)
x = 9
b)
x = 28
c)
x = 7
d)
x = 63
50.
Which side length corresponds with EF?
a)
MN
b)
LM
c)
OL
d)
EH
51.
Sides that are in the same position are called
a)
Corresponding Sides
b)
Corresponding Angles
c)
The Same
d)
Congruent Sides
52.
Tell whether the two figures are similar. Explain your reasoning. (Hint: are they proportional?)
a)
Yes, similar because they are the same shape and side lengths are proportional.
b)
No, not similar because they are the same shape, but side lengths are not proportional.
c)
Yes, same shape
d)
No, different sizes
53.
Angles in the same position are called
a)
Corresponding Sides
b)
Corresponding Angles
c)
The Same
d)
Congruent Angles
54.
All corresponding sides are proportional (same ratio) in similar figures.
a)
True
b)
False
55.
Sara can type 90 words in 4 minutes. About how many words would you expect her to type in 10 minutes at this rate? (Use proportion)
a)
900 words
b)
180 words
c)
225 words
d)
360 words
56.
Solve the proportion:
a)
4
b)
8
c)
14
d)
10
57.
The pair of figures is similar. Find the missing side.
a)
x = 20
b)
x = 12
c)
x = 5
d)
x = 4
58.
The pair of figures is similar. Find the missing side.
a)
x = 10
b)
x = 4
c)
x = 2
d)
x = 5
59.
The pair of figures is similar. Find the missing side.
a)
x = 1
b)
x = 3
c)
x = 9
d)
x = 5
60.
Find missing side
a)
5
b)
7
c)
9
d)
11
61.
Find missing side
a)
5
b)
7
c)
9
d)
11
62.
Solve for X.
a)
2 ft
b)
3 ft
c)
4 ft
d)
6 ft
63.
Find side length X.
a)
30
b)
25
c)
15
d)
40
64.
Find side length X.
a)
16
b)
18
c)
2.4
d)
15
65.
Find the missing side length.
a)
32
b)
35
c)
20
d)
16
66.
Find the missing side length.
a)
2
b)
4
c)
3
d)
6
67.
Find the missing side length.
a)
9
b)
8
c)
6
d)
12
68.
Find the missing side length.
a)
16
b)
12
c)
35
d)
15
69.
Solve for x.
a)
21
b)
14
c)
12
d)
18
70.
Solve for x.
a)
8
b)
6
c)
10
d)
12
71.
Solve for x.
a)
10
b)
18
c)
20
d)
12
72.
Solve for x.
a)
14
b)
21
c)
15
d)
10
73.
What is the measure of x?
a)
12
b)
15
c)
6
d)
9
74.
The pair of figures is similar. Find the missing side.
a)
x = 9
b)
x = 28
c)
x = 7
d)
x = 63
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